Document Type

Journal Article

Role

Author

Standard Number

1539-3755

Journal Title

Physical Review E

Volume

80

Issue

5

First Page

056207

Last Page

056213

Publication Date

2009

Abstract

Embeddings are diffeomorphisms between some unseen physical attractor and a reconstructed image. Different embeddings may or may not be equivalent under isotopy. We regard embeddings as representations of the attractor, review the labels required to distinguish inequivalent representations for an important class of dynamical systems, and discuss the systematic ways inequivalent embeddings become equivalent as the embedding dimension increases until there is finally only one “universal” embedding in a suitable dimension.

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